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Thursday, December 29, 2011

One of the computers in my house came to the end of its useful life recently. In my house, that means ordering a new computer from Dell. Since I’m a tech guy and have techie friends, I’ve heard time and again how I can save money by buying cheap components and putting the PC together myself. But I’d rather leave it to Dell to put the system together and pay a little extra, but not too much extra.

I prefer to buy online, but the Dell web site didn’t allow me to make all the choices I wanted. This meant having to make a call to Dell. This also meant having to turn down all the high-margin items available as add-ons.

I was pleasantly surprised when the salesperson didn’t press me on an extended warranty after I turned it down; she just went on with the list of other choices. However, when we came to the end, she began a script: “You know sir, you’re buying an expensive computer...”.

For a mere $119 I could extend the standard warranty from 1 year to 2 years. After I turned down this offer a miracle happened and the extra year of warranty dropped to $79 in 10 seconds. After I refused again, it took only 10 more seconds for it to drop to $60. Yet another refusal by me didn’t create any further drops in price.

I don’t know what an extra year of warranty costs Dell, but I’m guessing that it’s much less than $60. This makes the original price of $119 seem like a big gouge.

Tuesday, December 27, 2011

I’m a victim of marketing. The title of the book Train Your Brain to Get Rich by Aubele, Freeman, Hausner, and Reynolds caught my eye, but the title is misleading. The additional words on the cover, “the simple program that primes your gray cells for WEALTH, PROSPERITY, and FINANCIAL SECURITY,” just add to the misdirection. This book isn’t really about money.

As I read through the first quarter of the book, I kept waiting for the financial aspects to begin, but by the hundredth page I suspected that they never would begin, and as I finished the last page, my suspicion was confirmed.

This book is really about brain health and the benefits of such things as a positive attitude, meditating, exercise, sleep, and healthy eating. The superficial financial parts of the book could just as easily be replaced with “train your brain to play better tennis.”

The financial references actually seem as though as though they were added after the fact by a different writer. It’s as though someone took a completed book and added variants of “to get rich” and “your way to wealth” to all the chapter titles. The financial references inside the book are equally superficial.

There are many examples of this financial superficiality within the book, but I’ll give just one. A section that discusses the brain benefits of dreaming is titled “Dream Yourself Rich”. I would have preferred “Dream Yourself to Killer Abs”.

In an effort to say something positive, I found two things. In one section the authors recommend a focus on buying experiences rather than material things, which seems like very good advice. They also quoted studies showing that while caffeine boosts simple mental processes, it does not seem to help with creative pursuits or “thinking beyond the basics.”

Don’t get too positive about what you might learn, though. The reader is also treated to the following claim: “When you’ve identified an intention, focused on it, and made a clear, committed decision to act upon your intention, your mind will open up the universal floodgates, bringing all the resources you need, sometimes in seemingly mysterious or impossible ways.” Thanks for that.

I can imagine a whole series of books about different subjects: “train your brain to make people like you,” or “train your brain to find a girlfriend.” The great thing is that it would probably take only 15 minutes to replace the financial buzzwords to create each new book.

Friday, December 23, 2011

This will be the last regular post until next year. I may write one or two before then if the mood strikes. To all my readers, I wish you happy holidays and all the best in the new year.

Where Does All My Money Go? breaks down the effect of mutual fund fees on a 25-year investment. Check out the spreadsheet that lets you enter your own inputs to see how much of your money goes to your advisor, the dealer, and the fund company.

Gail Vaz-Oxlade conducted a poll to find out how much people could reduce their monthly expenses if they had to. The most striking thing about this poll is that the highest category is “15% or more”. I could reduce my expenses by 50%. If I absolutely had to, I could go further by moving my family somewhere cheaper. I think people have a misguided sense of the distinction between necessities and wants. Necessities are food, simple clothing, shelter, education, and not much more.

Canadian Couch Potato interviews Vanguard representatives about their entry into Canadian ETFs and what new ETFs may come in a second wave. I’m particularly interested in U.S. and foreign stock ETFs without currency hedging. See part 2 of the interview as well.

The Blunt Bean Counter shows that there is no advantage to earning income in a corporation because of the way that dividend taxation is integrated with personal taxes. I wonder if maybe there are certain narrow situations where using a corporation can be used to smooth personal income between years. One strange situation would be two people who run a company by each working every other year. They would prefer to declare $75,000 every year rather than $150,000 every other year.

Tom Bradley takes on the claims that the world's financial troubles are “different this time”. Ironically, one of the ways that things remain the same is that people tend to think that present conditions are different from the past.

My Own Advisor had some fun making a financial version of Christmas poetry.

Thursday, December 22, 2011

Come January, I’m expecting a huge raise. Most workers get a huge raise at the start of a new year, but they don’t realize it. In the last days of the year, you are taxed at your top marginal rate, but in January the slate is clean and your income is untaxed for a while.

You won’t see any of this on your pay stub, though. Payroll taxes are designed to smooth out the effect I’m talking about by predicting your final taxable income and taking equal amounts of tax off each pay. But your real taxes are based on your actual income using progressive percentages.

For a person earning $100,000 per year in Ontario, after-tax pay at the end of this year is $28.92 per hour, but will rise to $51.11 per hour starting in January (based on 37.5 hours per week and 365.25 days per year). Of course, it will then drop off over the course of 2012.

For most of us who collect a regular income for the whole year, none of this makes much difference, but for those who work irregularly of for irregular pay rates, this effect can be important.

For example, if you’re planning to quit your job to live off your savings for a few years and see the world, it’s better to wait until March than to quit in December. This way you’ll get paid during the high-income period at the start of the year.

If you’re planning to do something that will cause a big change in your income, it pays to understand our progressive tax system and how it affects your final tax bill.

Wednesday, December 21, 2011

"I see via your magazine insert I can order a year's subscription for Ontario for $53.62 (tax included) whereas I just recently paid $70.86 to renew mine! While I can understand the ‘bonus gift’ difference, I am quite upset that you are gouging (over 30 %!) a long time subscribing customer (over 30 years)."

Jerry went on to demand a refund of the difference, and Maclean’s promised he would get it in 4 to 6 weeks. Of course, the other loyal customers who don’t bother to complain won’t get this refund. Most people believe that loyal customers deserve to be well-treated, but companies seek profits. Apparently, Maclean’s magazine has decided that the most profitable approach is to draw people in with low prices and hope they keep subscribing at higher prices. My guess is that they are right.

This doesn’t mean that I think loyal customers deserve poor treatment; I just don’t think that discussions of what we deserve are relevant (except as a way to extract a refund). Businesses must seek profits to survive. If enough Maclean’s customers stop subscribing because they don’t like paying more than new customers, then Maclean’s will change its practices. The same is true of Maclean’s parent company, Rogers. However, my guess is that more people are willing to give up a magazine for a principle than are willing to give up their television and internet.

Unless more people start to vote with their wallets, expect loyal customers of most businesses to continue to pay higher prices than fickle customers who pay attention to prices. In the mean time, people like Jerry can get lower prices by complaining.

Tuesday, December 20, 2011

We often hear of unions seeking pay parity with other workers. Invariably, a pay raise and possibly some back pay are required to right the supposed unfairness. No doubt there are legitimate cases, but I suspect that most are not.

My direct experience is mostly with programmers. Organizations have different philosophies when it comes to paying programmers. Some seek the best talent they can find and give them above-average pay. Most offer average pay and get average talent, and still others offer low pay and try to get by with whoever will work for them.

It is too easy for programmers at one company to look at another company’s pay scales and complain. The truth is that most complainers would be rejected if they tried to get a job with the higher-paying company. Superficially, all programmers do similar work, but when we get down to details it is normal for one company’s programmers to be far superior to another company’s programmers. When this is true, demands for pay parity make little sense.

With this experience as a backdrop, I tend to be skeptical of any claim that one group of workers does the same work as another and deserve pay parity. If this were true, why aren’t members of the lower-paying group leaving to get jobs with the higher-paying group? The answer is often that the better workers actually do this and thus create a meaningful difference in talent between the two groups.

Monday, December 19, 2011

Dan Hallett at The Wealth Steward accused mutual fund critics of missing the big picture when they focus their criticism on high MER costs. His main point is not so much that MERs are not a problem but that there are other important ways that investors lose money. He claims that one of these ways that investors lose money is due to a volatility drag that comes with periodic investments or dollar-cost averaging (DCA). I’ve done a couple of experiments and can’t find any evidence that this volatility drag exists. In fact, DCA has a slight edge over lump-sum investing.

Hallett explains volatility drag as follows:

“You’ve no doubt scratched your head at why a portfolio’s long-term performance hasn’t quite lived up to expectations. It’s likely that volatility drag is one of the big culprits. ... If a mutual fund reports a 7 percent 10-year rate of return, for example, the only way to have achieved that precise result was to invest at the beginning of that period, hold for the full decade and have no buys or sells in between. ... The investment industry has long preached the benefits of investing a regular dollar amount so that you buy more units of a fund when the price goes down and fewer when it’s up. This intuitive argument just doesn’t hold. ... Stock fund investors, however, might see returns that are 150 basis points (or 1.5 percentage points) less than published performance just from the fact that there are regular transactions over time.”

In the first experiment, I looked at rolling 15-year periods. For each period, I calculated the average compound return from investing a lump sum at the beginning of the period and holding it for the full 15 years. The average compound return across all periods was 6.19%.

Then for each period, I considered the case where an investor makes an equal size investment at the start of each year for 15 years. For each period I calculated the internal rate of return (IRR). With this method of calculating return, we don’t penalize DCA for having less money invested in the early years. Across all of the 15-year periods, the average return was 6.52%, which is more than the average lump-sum return.

Of course, this victory for DCA may be just a quirk of the particular set of returns I used. While the DCA approach edged out the lump-sum approach on average, the results for individual 15-year periods varied. The full range was from DCA winning by 3.07% from 1973 to 1987 (inclusive) to DCA losing by 2.38% from 1978 to 1992 (inclusive).

The reason why DCA performs differently from lump-sum investing is that with DCA there isn’t much money invested in the early years. If the early years have better returns than later years, then lump-sum investing will win, and if the early years have lower returns than later years, then DCA will win. The fact that the TSX was down nearly 40% in 1973-74 and up nearly 60% in 1978-79 tells us why DCA beat lump-sum starting in 1973, but lost starting in 1978.

Experiment 2

To factor out this dependence on the order of returns, I did a second experiment. I used 12 years of TSX return data from 1999 to 2010 inclusive. For every possible reordering of the 12 years of returns I calculated the DCA return. (There are nearly half a billion cases and it took a program 12 minutes to check them all. To do the same for 15 years of returns would have taken about 3 weeks, and I’m not that patient.)

The DCA return results ranged from -1.81% to 15.82% with an average of 6.55%. The lump sum compound return is the same in every case: 6.27% per year. So we see that DCA returns can differ from lump-sum returns by quite a bit, but on average, the DCA returns are slightly better. In fact, the DCA return was higher than the lump-sum return in 52.3% of the cases.

Conclusion

I can’t find any evidence that Hallett’s volatility drag exists. Either one of us is wrong, or we are calculating different things. There is another type of volatility drag that comes from compounding, but this applies to both lump-sum investing and dollar-cost averaging.

For investors who are enthusiastic about dollar-cost averaging, these results do not apply to the case where you have a lump sum and choose to invest it slowly over a period of time. This is because of the opportunity cost of the lost returns on money waiting to be invested.

Saturday, December 17, 2011

It pays to be wary of investment scams. The well-done 3-minute video below hits the high points for how to protect yourself. It was created by the (deep breath) U.S. Financial Industry Regulatory Authority (FINRA) Investor Education Foundation.

Glenn Cooke of InsureCan Inc. was our top bidder of $100 in the Blogger’s for Charity auction. Glenn will be contributing a guest post on this blog on 2012 Jan. 17. Thanks to all the bidders. Hopefully, they will contribute their bid amounts to their favourite charities anyway – winter is a tough time for those in need.

Friday, December 16, 2011

The highest bid so far in the bloggers for charity auction for a post on this blog (see here for details) is $100. Bidding will close tonight at 11:59 pm EST. I will update this note with further bids.

Jason Zweig has some examples of small investors being harmed by strange results when trading stocks. He gives some suggestions for protecting yourself against these infrequent but costly problems.

Ellen Roseman thinks that the Rogers-Bell collaboration to buy a majority stake in Maple Leaf Sports and Entertainment is bad for Canada. I agree with her. These companies' near monopoly status allows them to treat their customers poorly to increase profit. If anything we should be looking at breaking up these companies to improve competition.

Canadian Mortgage Trends says that 6.5% of Canadian mortgagors currently pay more than 40% of their income to service debts, but that increasing interest rates would drive that percentage higher.

Money Smarts finds that Canadian Tire's "1% rewards" card actually gives a much lower reward than advertised due to truncating purchase prices. Maybe they don’t have any computers and don't like working with too many digits. The next time you're there to buy something for $129.99, try offering them $100 just to keep things simple.

Wealthy Boomer weighs in on the 2-page Fund Facts that Canada's fund companies now provide for each fund.

Canadian Capitalist says that if you're unhappy with high MERs, you should vote with your wallet.

Gail Vaz-Oxlade explains a retailer trick that gets us to pay more. I think this one has worked on me many times.

Potato gives a thorough and convincing explanation of why the solar electricity MicroFIT program exists despite the fact that it loses the government money.

Big Cajun Man has some snappy answers to (stupid) financial questions modeled after Mad Magazine. A couple of them had me laughing out loud.

Million Dollar Journey edges ever closer to his goal of a million-dollar net worth. Will he shut down his blog when he gets there? I hope not.

Preet Banerjee says to hold on to your long-term investing strategy even when it hasn't performed well lately.

Larry MacDonald says that the European Central bank could end the EU crisis right now by announcing that they will print enough Euros to keep indebted EU members' borrowing costs down. However, the central bank is using the crisis to try to get indebted EU members to stop borrowing wildly.

Thursday, December 15, 2011

My employer recently moved to a hoteling system where nobody has a fixed desk. We just take our laptops out of a locker and pick a desk each day. This has its advantages and disadvantages, but one side effect is that it is much more difficult to have great piles of paper. I've had to throw away unimportant papers and scan the important ones. This elimination of paper has been very freeing for me, and it occurred to me that this way of thinking would be good for Library and Archives Canada as well.

Certain documents are of such great historical significance that they it makes sense for taxpayers to pay to preserve them. However, many documents held by Library and Archives Canada could simply be scanned, the electronic copies be made available to Canadians free on the internet (assuming their copyrights have run out), and then the original documents could be sold to collectors.

I wouldn't want to lose great works of fiction written by Canadians, but all I need is an electronic copy. Then anyone who wants it on paper could simply print it themselves. I don't see why taxpayers should pay to house the physical books in an expensive building. Library and Archives Canada has a service making it possible to get electronic copies of documents now, but you have to pay between 20 and 80 cents per page (the web page explaining these charges has disappeared since this article was written). Why not just scan everything once and be done with it?

I used to want paper copies of documents to truly feel like I possessed them. I'm over that now. Data on the internet has a permanence that physical objects like paper can't match. Combine this with the fact that electronic copies would be far more accessible to all Canadians, and the idea of scanning all historical documents is obviously the right direction.

Wednesday, December 14, 2011

The typical person will invest for many years, but we express investment costs with yearly percentages that are misleadingly low. I propose that for recurrent costs that accumulate, we use an investing horizon of 25 years to express these figures.

For example, instead of talking about a fund's MER, we would talk about its MERQ (Management Expense Ratio per Quarter century). This would give investors a better feel for the effect of recurring costs. In another example, if an investor's portfolio concentration creates a drag on returns, we should look at the effect over 25 years rather than just one year.

If you can handle your own investments, then you only have to give iShares 12.4% of your money over 25 years. Going even further, the MERQ of Vanguard's Total Stock Market ETF (VTI) is only 1.73%. Seeing cost figures ranging from under 2% up to 49% ought to make investors think.

In another example, I recently concluded that a portfolio of 20 randomly-selected stocks would underperform the index by 0.51% per year based on a paper by Meir Statman. If the stocks owned by dividend investors are no better than random, then a 20-stock portfolio would lose 0.51% per year to the index due to increased volatility. Based on some of the comments on that article, it seems that investors are unconcerned about such a small percentage of drag. But, if we say that the drag (dragQ?) is 12% over 25 years, it seems more troubling. Of course, most dividend investors don't believe that their stocks are no better than random, but that's a discussion for another day.

Even if the world doesn't like the idea of adding a "Q" to the end of MER and other measures, I think the fundamental idea of taking a longer view would help investors.

Tuesday, December 13, 2011

Big economic events, popularized as “black swans”, are known to happen more often than standard economic theory predicts. However, it’s not easy for most investors to figure out what they should do with this information other than to be vaguely worried. One important implication is that leverage is more dangerous than it appears.

Leverage just means borrowing to invest. If you invest $50,000 and it goes up 10%, you make $5000. But if you had borrowed another $50,000 at 4% interest, you’d have made $10,000 less $2000 in interest for a profit of $8000. When investments are rising, leverage is a wonderful thing. However, when investments are dropping, leverage magnifies losses. There is even the possibility of going completely broke if the value of your investments drops below the amount you owe.

In most cases where investors use leverage, they can weather minor storms by paying off the leverage loan with employment income. This way they can wait out stock market tumbles until prices rebound. However, a big enough stock market crash might knock a leveraged investor out of the market completely leaving huge losses. It’s tough enough to watch a portfolio half in stocks get hammered, but it’s another thing to be 200% in stocks and watch them plummet.

Proponents of leverage often talk of Sharpe Ratios and the optimal amount of leverage. These formulas are based on the standard Bell curve and do not give results that are useful for most investors. Be very wary of leverage.

Monday, December 12, 2011

Right now in Canada you usually pay the same price to a retailer for goods and services whether you pay by cash, debit, or credit. On the surface this seems like a good thing. However, when we scratch the surface, we see inefficiencies that boost prices. Planned changes to these price rules could create different pricing for different payment methods, but whether consumers will benefit is still unclear.

When you pay with a credit card, the retailer has to pay between 1.5% and 3% of the transaction amount to the credit card company. The cost of all the wonderful credit card reward schemes we enjoy comes out of these fees charged to retailers.

Retailers have to raise their prices to compensate for the fees they pay to credit card companies. The catch is that everyone has to pay these higher prices, even those who pay with cash. In effect, people who pay cash are subsidizing the credit card rewards and cash-back schemes. But only some of the retailer fees flow back to consumers as rewards; the rest goes to banks and credit card companies.

Retailers are upset about new credit cards that require them to pay ever-higher fees. These higher fees pay for the increasingly generous credit card rewards consumers enjoy. But more of these fees are kept by banks and credit card companies, which causes the prices of goods and services to rise.

So, there are two problems. One is cash-paying consumers unfairly having to subsidize credit card users. The other is the growing fraction of transactions that get retained by banks and credit card companies that must lead to higher prices for consumers.

Retailers argue that they should be able charge consumers extra for credit card purchases. On the surface this would seem to solve both problems. Retailers in competitive markets would advertise slightly lower prices. This would end the subsidy by cash-payers, and credit card users would pay for the credit card fees. The high-fee credit cards would suddenly be less desirable to consumers if they had to pay 3% extra for each transaction. Cash, debit, and lower-fee credit cards would suddenly look much better.

However, why should we think that retailers would pass on just their actual costs for credit card fees? Why wouldn’t they charge much higher fees if they could get away with it? Consumers are driven by advertised prices and may not be as sensitive to extra charges at the point of sale. In the absence of rules to prevent this kind of abuse, particularly by monopolies and near-monopolies, there is no reason to believe that consumers would be any better off if retailers could charge extra fees for credit card transactions.

The Competition Bureau is challenging the rules credit card companies impose on retailers preventing them from charging extra fees for using credit cards. There is a lot at stake and it isn’t clear how much freedom retailers might get to charge extra fees. If retailer freedom is limited, consumers are likely to benefit, but the situation is less clear if retailers are free to add surcharges as they please.

Boomer and Echo describes how debit cards draw people into high banking fees.

Canadian Couch Potato has a vivid illustration of how investment marketers could paint very different pictures by just taking the window in time for quoting investment returns and shifting it by 3 months.

Thicken My Wallet has an amusing little story that links Bobby Bonilla and the New York Mets with Bernie Madoff. You won't be surprised to learn that this story involves a poor investment decision.

Thursday, December 8, 2011

Nassim Taleb gets much credit for popularizing the idea that big economic events, so-called “black swans,” occur more frequently than standard economic theory predicts. The initial work was actually done by the “father of fractals,” Benoit Mandelbrot.
Physicists have studied detailed market data and have now concluded that Mandelbrot was right. (Hat tip to the Stingy Investor for pointing me to this article.)

The bigger the market move we contemplate, the lower the chances that it will happen. However, these probabilities shrink much more slowly than standard economic theory predicts. In standard economic theory based on the normal distribution, if a move has a 1 in 1000 chance of happening, a move twice as large has less than a 1 in a billion chance of happening. In Mandelbrot’s model as confirmed by the physicists, the bigger move has about a 1 in 8000 chance; each doubling in move size reduces the odds by 8 times.

For conditions of low market volatility, standard theory and Mandelbrot’s model agree fairly well, but when it comes to the possibility of big upheavals, standard theory is just plain wrong.

Wednesday, December 7, 2011

The top bid so far in the charity auction for a guest post on Michael James on Money is $100. See here for more details on the auction. Keep those bids coming.

Credit card companies, retailers, and other businesses have jumped on the loyalty points bandwagon. We accumulate all sorts of different points, and some of us manage to redeem points for various goods and services. I tend to look at these points as a kind of currency.

Businesses are issuing their own brand of currency that they give their customers in return for making purchases with actual money. The problem for consumers is that these businesses control the rules for this currency and can devalue it at any time by adding various restrictions and changing the number of points needed to redeem a “reward”.

Viewed this way, it becomes apparent that many reward points systems aren’t worth the bother, but this isn’t likely to change consumer behaviour. The innumerate masses love their points. It’s true that some points systems have real value and are worth the trouble, but this is the exception rather than the rule.

Tuesday, December 6, 2011

Vanguard's first 6 Canadian ETFs begin trading today (see the list below). Note that the MERs consist of slightly more than the management fees listed. The most interesting of these to me is VCE as a potential replacement for XIU for Canadian stocks. However, I plan to wait and see that all goes smoothly in the first few months of trading. I have little interest in the bleeding edge when it comes to new securities.

Monday, December 5, 2011

A very popular method of investing is to build a portfolio of individual stocks with a solid history of dividend payments. Dividend investors tend to believe that this approach will beat index investing, and index investors believe that dividend investors have sub-optimal portfolios.

Although dividend investing tends to be quite passive in the sense that it involves infrequent trading, it is at least a little bit active in the sense that dividend investors choose individual stocks. Any time you choose an active investing strategy, it makes sense to know how much your strategy is likely to underperform the market averages in the event that your strategy is little better than random.

So, if we begin with the premise that index investors are right and that dividend investors are likely to underperform, how much lower are their returns expected to be? To answer this question, I dug up an old paper by Meir Statman: How Many Stocks Make a Diversified Portfolio? In it he reprints a table of the number of stocks in a portfolio and its expected standard deviation from a book by Elton and Gruber. Here are a few lines from this table:

The volatility drag on compound returns is half the square of the standard deviation. So, here are the volatility drag numbers:

1 stock: 12.12%
10 stocks: 2.86%
20 stocks: 2.35%
All stocks: 1.84%

Compared to index investing where portfolios contain all stocks, smaller portfolios have the following excess volatility penalties on compound returns:

1 stock: 10.16%
10 stocks: 1.02%
20 stocks: 0.51%
All stocks: 0%

So, if a dividend investor owns 10 stocks and they are essentially randomly-selected, the investor is giving up 1.02% per year in returns. At 20 stocks, the penalty is only 0.51%.

Of course, dividend investors don’t believe that their stock choices are random. But even if they are wrong, a portfolio of 20 dividend-paying stocks from a wide range of different industries is only giving up about 0.5% per year compared to index investing (not counting taxes). Giving away returns is never a good idea, but many active investing approaches have higher expected losses to the index than just 0.5%.

Friday, December 2, 2011

Wealthy Boomer takes off the gloves in an exchange with Investors Group over sky-high mutual fund MERs and a questionable commitment to Canadians’ financial literacy. The truth is that Investors Group profits greatly from their clients’ lack of understanding of important investing facts.

Big Cajun Man created an amusing flowchart of financial planning in families. I fear that many people follow this flowchart.

The Blunt Bean Counter explains that while he is moving to passive investing, he plans to be a stock-picker for a small fraction of his portfolio for the excitement.

Canadian Capitalist likes Ally's high savings account interest rates and wonders why it isn't more popular.

Retire Happy Blog explains some model investment portfolios. He gives a range from conservative to aggressive. There are higher levels, though. If you borrow to invest, such as with the Smith Manoeuvre, you are moving into the hyper-aggressive range. I think leveraged schemes might be less popular if people understood how risky they are.

Larry MacDonald reviews David Trahair's new book Crushing Debt: Why Canadians Should Drop Everything and Pay Off Debt. The Wealthy Boomer reviewed this book as well.

Thursday, December 1, 2011

Calculating the total return of a collection of investments is a simple matter of adding up or averaging the returns of the individual investments, right? In reality, the right way to "add" or "average" returns depends on the context.

Suppose that investment A stayed flat for two years (0% return each year), and investment B fared much better returning 20% each year for both years. Suppose further an investor splits $1000 between A and B in the first year, then rebalances and again splits his money between A and B in the second year:

To start:

A $500
B $500

After year 1:

A $500
B $600

The total is $1100 for a 10% return. So we see that correct overall return is the average of 0% and 20%, namely 10%. This investor will get another 10% return in the second year and will end up with $1210 for a total return of 21% after two years.

Note that the total return is not just 10% + 10% = 20%. In this case we have to "add" the returns using compounding: 1.10 x 1.10 - 1 = 21%.

Consider a second investor who owns only investment A for one year and then only investment B for the second year. We might think that this investor will get an average return of (0% + 20%)/2 = 10%, but he does not. This investor will be left with $1200 for an overall return of 20%. But this doesn't work out to the 10% per year that the first investor got. The second investor's average return is 9.54% per year. When you compound this return for two years, you get his 20% total return for the two years.

This isn't just an academic exercise. Lenders use this against us all the time. If you get a monthly car loan at 6% per year, the actual rate is 0.5% per month. They call this "simple interest". In reality they calculate the monthly rate as though they were going to use simple interest (divide by 12), but then they compound it. If you multiply 1.005 by itself 12 times you get the real yearly rate that you’re paying: 6.17%. The difference isn't huge, but it's still extra money out of your pocket.

Understanding when to add returns and when to compound them is at the core of why higher portfolio volatility leads to lower long-term investment returns. Any time you hear someone talk about the average return of some type of investment you should ask what kind of average was used.